// Exercise 4.4.28 (Solution published at http://algs4.cs.princeton.edu/)
package algs44;
import stdlib.*;
import algs13.Stack;
import algs42.Topological;
/* ***********************************************************************
 *  Compilation:  javac AcyclicLP.java
 *  Execution:    java AcyclicP V E
 *  Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Topological.java
 *  Data files:   http://algs4.cs.princeton.edu/44sp/tinyEWDAG.txt
 *
 *  Computes longest paths in an edge-weighted acyclic digraph.
 *
 *  Remark: should probably check that graph is a DAG before running
 *
 *  % java AcyclicLP tinyEWDAG.txt 5
 *  5 to 0 (2.44)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->0  0.38
 *  5 to 1 (0.32)  5->1  0.32
 *  5 to 2 (2.77)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->7  0.37   7->2  0.34
 *  5 to 3 (0.61)  5->1  0.32   1->3  0.29
 *  5 to 4 (2.06)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93
 *  5 to 5 (0.00)
 *  5 to 6 (1.13)  5->1  0.32   1->3  0.29   3->6  0.52
 *  5 to 7 (2.43)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->7  0.37
 *
 *************************************************************************/

public class AcyclicLP {
	private final double[] distTo;          // distTo[v] = distance  of longest s->v path
	private final DirectedEdge[] edgeTo;    // edgeTo[v] = last edge on longest s->v path

	public AcyclicLP(EdgeWeightedDigraph G, int s) {
		distTo = new double[G.V()];
		edgeTo = new DirectedEdge[G.V()];
		for (int v = 0; v < G.V(); v++) distTo[v] = Double.NEGATIVE_INFINITY;
		distTo[s] = 0.0;

		// relax vertices in toplogical order
		Topological topological = new Topological(G);
		for (int v : topological.order()) {
			for (DirectedEdge e : G.adj(v))
				relax(e);
		}
	}

	// relax edge e, but update if you find a *longer* path
	private void relax(DirectedEdge e) {
		int v = e.from(), w = e.to();
		if (distTo[w] < distTo[v] + e.weight()) {
			distTo[w] = distTo[v] + e.weight();
			edgeTo[w] = e;
		}
	}

	// return length of the longest path from s to v, -infinity if no such path
	public double distTo(int v) {
		return distTo[v];
	}

	//  is there a  path from s to v?
	public boolean hasPathTo(int v) {
		return distTo[v] > Double.NEGATIVE_INFINITY;
	}

	// return view of longest path from s to v, null if no such path
	public Iterable<DirectedEdge> pathTo(int v) {
		if (!hasPathTo(v)) return null;
		Stack<DirectedEdge> path = new Stack<>();
		for (DirectedEdge e = edgeTo[v]; e != null; e = edgeTo[e.from()]) {
			path.push(e);
		}
		return path;
	}



	public static void main(String[] args) {
		In in = new In(args[0]);
		int s = Integer.parseInt(args[1]);
		EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);

		AcyclicLP lp = new AcyclicLP(G, s);

		for (int v = 0; v < G.V(); v++) {
			if (lp.hasPathTo(v)) {
				StdOut.format("%d to %d (%.2f)  ", s, v, lp.distTo(v));
				for (DirectedEdge e : lp.pathTo(v)) {
					StdOut.print(e + "   ");
				}
				StdOut.println();
			}
			else {
				StdOut.format("%d to %d         no path\n", s, v);
			}
		}
	}
}